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Simulation of electronic structure Hamiltonians using quantum computers
Open accessAbstract
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient methods for the exact simulation of quantum systems on classical computers presents a limitation of current computational approaches. We report, in detail, how a set of pre-computed molecular integrals can be used to explicitly create a quantum circuit, i.e. a sequence of elementary quantum operations, that, when run on a quantum computer, obtains the energy of a molecular system with fixed nuclear geometry using the quantum phase estimation algorithm. We extend several known results related to this idea and discuss the adiabatic state preparation procedure for preparing the input states used in the algorithm. With current and near future quantum devices in mind, we provide a complete example using the hydrogen molecule of how a chemical Hamiltonian can be simulated using a quantum computer.
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“The time the quantum computer must remain coherent is determined by the necessity of O(p−1) successive applications of , each of which can require on the order of millions or billions of quantum gates for practical applications1719, as compared to the tens to hundreds of gates achievable in the short term.”
From A variational eigenvalue solver on a photonic quantum processor (2014) · cites this paper as [17]
Experimental — accuracy not yet measuredIn the citing paper
“Indeed, there are already proposals 200 for NISQ algorithms based on variational principles 201,202 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [201]
In the citing paper
“It is remarkable that the standard quantum-circuit treatment (e.g. see Ref.47) for implementing each involves as many as 2N two-qubit gates for simulating N fermionic modes; in our protocol one needs only two Mølmer-Sørensen gates, which are straightforwardly implementable with current trapped-ion technology.”
From From transistor to trapped-ion computers for quantum chemistry (2014) · cites this paper as [47]
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A variational eigenvalue solver on a photonic quantum processor
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Metadata
- Authors
- Whitfield, J. D., Biamonte, J., & Aspuru-Guzik, A.
- Affiliations
- Harvard University (US)
- Corresponding author
- Whitfield, James D.
- Biamonte, Jacob
- ORCID
- Biamonte, Jacob
- Venue
- Molecular Physics
- Publisher
- Informa UK Limited
- Published
- 2011-03-10
- Volume
- 109
- Issue
- 5
- Pages
- 735-750
- ISSN
- 0026-8976 (ISSN-L)
- 1362-3028
- OpenAlex
- W2103373613
- Cited by
- 472
- References
- 36
- Citations by year
- 2026: 33 · 2025: 54 · 2024: 54 · 2023: 64 · 2022: 49 · 2021: 36 · 2020: 43 · 2019: 23 · 2018: 29 · 2017: 13 · 2016: 14 · 2015: 14 · 2014: 19 · 2013: 11 · 2012: 12
- FWCI
- 13.55
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Molecular Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Engineering and Physical Sciences Research Council (EP/G003017/1)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum phase estimation, quantum circuits, molecular integrals, adiabatic state preparation, molecular hydrogen, quantum chemistry, quantum computing
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